jrssRecent rapid developments in information technology have enabled the collection of
high-dimensional complex data, including in engineering, economics, finance, biology, and health sciences [1]}. High-dimensional means that the number of features is large and often far higher than the number of collected data samples. In many of these applications, it is desirable to find a small best subset of predictors so that the resulting model has desirable prediction accuracy [2]}, [3]}.
In this article, we recast the challenge of best subset selection in linear regression as a continuous optimization problem. We show that this reframing has enormous potential and substantially advances research into larger dimensional and exhaustive feature selection in regression, making available best subset selection when \(p\)  is well in excess of 1000s.
